A bow might be a deadly weapon in a skilled mans hand, but its not too usefull against heavy infantry with shields. Without the stakes and bad weather the english bowman at agincourt would never have beaten the french knights.
About the firearms discussion,
A weapon beeing able to kill people by penetrating their shields and their armour and inflicting huge wounds (The first firearms used quite big bullets, often made of lead causing deadly poisoning) is much more frightening than arrows which you can absorb which your shields. (Or at least have the illuson about it). Another point is the space bowman need to have. Firearms mad close shooting formations possible.